Modelling of Magnetosensitive Elastomers

Abstract

Magnetorheological elastomers (MREs), also referred to as magnetosensitive (MS) elastomers, are smart materials composed of micron-sized ferrous particles dispersed in a polymer matrix. Commonly, magnetic fields are applied to the polymer composite during cross-linking so that chainlike columnar particle structures can be formed and fixed in the matrix after curing. The unique characteristic of MRE is that its shear modulus can be continuously controlled by the external magnetic field (Gong et al., 2005). Shearing of the cured composite in the presence of the magnetic field causes particle displacement from their low energy state, thereby requiring additional work. This work rises monotonically with applied magnetic field, thus resulting in a field dependent shear modulus. It has been reported (Jolly and all., 1996) that the maximum increase in the shear modulus due to the MR effect is about 50–60% of the zero-field modulus, depending on the matrix elastomer. For hard elastomers like natural rubber the relative increase has typically been 30–40%. The field-induced modulus increase is substantial even at kilohertz mechanical frequencies (Ginder et al., 2002). Such properties make MREs promising in many applications in automotive industry as variable stiffness suspension systems and active damping components (Carlson & Jolly, 2000, Lerner & Cunefare, 2007, Kalio et al., 2007, Deng & Gong, 2007). To provide basic guidelines for designing and optimization of MR devices it is necessary to simulate the static and dynamic behaviour of magnetosensitive materials submitted simultaneously to the action of the mechanical loading and magnetic field. Modern design practices in the rubber industry are largely based on finite element simulations and the accuracy of these analyses relies on the ability of the used constitutive model to predict the mechanical response of the MS material. Nowadays the so–called magnetoelastic coupling is widely used for simulations of the reciprocal effect between the magnetic and the elastic field. In particular, the linear elastic behaviour is usually considered along with the linear or non linear magnetic properties. Most of the simulations are based on very simple linear magnetoelastic models defined by using the magnetic forces as loads. In these weak-coupling models the magnetic equations and the mechanical equations are solved separately. More accurate linear elastic models, based on the strong coupling, solve simultaneously the governing equations of the problem (Belahcen, 2004, Hasebe et al., 2007, Zhou & Wang, 2006a,b). However, elastomers exhibit strongly nonlinear elastic behaviour and undergo large deformations. The truthful magnetoelastic models of MS elastomers should incorporate the